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Mfp4 Help!!!!!

These AQA questions are annoying, espically the end ones. There impossible!

Also, I think they suspect the person to have a brain wave or something.

5. The transformation with matrix TT, where T=[212−2]T=\begin{bmatrix} 2 & 1 \\ 2 & -2 \end{bmatrix}, maps the point (x,y) onto the point (x',y') where [x′y′]=T[xy]{\begin{bmatrix} x' \\ y' \end{bmatrix} }= T{\begin{bmatrix} x \\ y \end{bmatrix}}

(a) Find the equation of the image of the line y=3xy=3x under the transformation.
(b) Find also the equations of the lines through the origin which are turned through a right angle about the origin under this transformation.

I can do part (a), however I have no clue what I'm doing just that it gives the right anwser. Basically expand T and then have y'=3x', then solve by substituation.

However, part (b) I don't know where to start or what to do. I need help, can somebody show the workings of the above. Because I'm like what?

P.S. The AQA book sucks.
Reply 1
Avatar for XAlonso
XAlonso
fp4 is wicked
Reply 2
Avatar for James
James
14
Since it's a linear map, you just require that (x',y') is perpendicular to (x,y) for any point (x,y) on the line. And the scalar (dot) product is a good test of that.

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